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| | To sum up, we have recognized the perfectly innocuous utility of admitting the abstract intermediate object <math>i,\!</math> that may be interpreted as an intension, a property, or a quality that is held in common by all of the initial objects <math>x_j\!</math> that are plurally denoted by the sign <math>y.\!</math> Further, it appears to be equally unexceptionable to allow the use of the sign <math>{}^{\backprime\backprime} i \, {}^{\prime\prime}</math> to denote this shared intension <math>i.\!</math> Finally, all of this flexibility arises from a universally available construction, a type of compositional factorization, common to the functional parts of the 2-adic components of any relation. | | To sum up, we have recognized the perfectly innocuous utility of admitting the abstract intermediate object <math>i,\!</math> that may be interpreted as an intension, a property, or a quality that is held in common by all of the initial objects <math>x_j\!</math> that are plurally denoted by the sign <math>y.\!</math> Further, it appears to be equally unexceptionable to allow the use of the sign <math>{}^{\backprime\backprime} i \, {}^{\prime\prime}</math> to denote this shared intension <math>i.\!</math> Finally, all of this flexibility arises from a universally available construction, a type of compositional factorization, common to the functional parts of the 2-adic components of any relation. |
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| − | ==Work Area==
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| − | <pre>
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| − | The word "intension" has recently come to be stressed in our discussions.
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| − | As I first learned this word from my reading of Leibniz, I shall take it
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| − | to be nothing more than a synonym for "property" or "quality", and shall
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| − | probably always associate it with the primes factorization of integers,
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| − | the analogy between having a factor and having a property being one of
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| − | the most striking, at least to my neo-pythagorean compleated mystical
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| − | sensitivities, that Leibniz ever posed, and of which certain facets
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| − | of Peirce's work can be taken as a further polishing up, if one is
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| − | of a mind to do so.
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| − | As I dare not presume this to constitute the common acceptation
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| − | of the term "intension", not without checking it out, at least,
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| − | I will need to try and understand how others here understand
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| − | the term and all of its various derivatives, thereby hoping
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| − | to anticipate, that is to say, to evade or to intercept,
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| − | a few of the brands of late-breaking misunderstandings
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| − | that are so easy to find ourselves being surprised by,
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| − | if one shies away from asking silly questions at the
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| − | very first introduction of one of these parvenu words.
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| − | I have been advised that it will probably be fruitless
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| − | to ask direct questions of my informants in such a regard,
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| − | but I do not see how else to catalyze the process of exposing
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| − | the presumption that "it's just understood" when in fact it may
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| − | be far from being so, and thus to clear the way for whatever real
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| − | clarification might possibly be forthcoming, in the goodness of time.
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| − | Just to be open, and patent, and completely above the metonymous board,
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| − | I will lay out the paradigm that I myself bear in mind when I think about
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| − | how I might place the locus and the sense of this term "intension", because
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| − | I see the matter of where to lodge it in our logical logistic as being quite
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| − | analogous to the issue of where to place those other i-words, namely, "idea",
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| − | capitalized or not, "impresssion", "intelligible concept", and "interpretant".
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| − | </pre>
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| | ==Document History== | | ==Document History== |
